
Application 1: Fraud Detection. fig:application illustrates an example of money-laundering crime. Dark gray vertices \(C_{1}\)  and \(C_{2}\)  are both criminal accounts. Other vertices represent intermediary accounts (white nodes) or agents (light gray nodes) which assist the criminals. Directed edges depict forged transactions or other money laundering activities. The shortest cycles reflect criminals' most efficient ways for money laundering. As a result, a high number of such cycles travel through the criminal accounts. For example, a cycle, starting from and ending with \(C_{1}\)  via \(A_{1}\)  \(M_{1}\)  \(C_{2}\) , demonstrates such a route. The more such cycles that pass through a vertex, the more probable it is that the individual will engage in money-laundering activities.
A pre-screening criterion for offenders might include a specified number of shortest cycles [1]}, [2]}. Additionally, such data can also be utilized to detect fraudulent transactions on an e-commerce platform [1]}, [4]}.
[5]} develops an expert system for automobile insurance fraud detection. A collision graph is constructed by considering automobiles as vertices and edges between two vehicles as collisions. Fraudulent components share some structural characteristics, one of which is the occurrence of short cycles. [6]} studies the similar problem. Their experiments demonstrate that detecting cycles is more effective in finding potential fraudulent groups than using other methods, such as leading eigenvector. [7]} applies the cycle detection problem to a fraud detection system of financial institutions and demonstrates its effectiveness.
